experimental chemistry - Differentiation between zinc, aluminium, and magnesium ions in solution

If I have three aqueous ionic solutions in which I know that the cation is $\ce{Al^3+}$, $\ce{Mg^2+}$, or $\ce{Zn^2+}$, how do I find out which is which?

I was thinking to add $\ce{OH-}$ in the form of $\ce{NaOH}$, or something else to produce a precipitate, and testing these precipitates in other liquids, but I'm not sure what other liquids to try.

Answer

First, you add sodium hydroxide to the three different solution. (Remember to safe some of the solution, because we need it for the next test.)

The zinc ion will react with the hydroxide ion in the sodium hydroxide solution to form zinc hydroxide which is white. So, you see white precipitate.

$$\ce{Zn^2+ +2 OH^- -> Zn(OH)2}$$

Adding more sodium hydroxide, the zinc hydroxide will form the zincate ion which is colourless. So, you will see a clear solution.

$$\ce{Zn(OH)2 + 2 OH^- -> Zn(OH)4^2-}$$

The aluminium ion will react with the hydroxide ion in the sodium hydroxide solution to form aluminium hydroxide which is white. So, you see white precipitate.

$$\ce{Al^3+ +3 OH^- -> Al(OH)3}$$

Adding more sodium hydroxide, the aluminium hydroxide will form aluminate ion which is colourless. So, you will see a clear solution.

$$\ce{Al(OH)3 + OH^- -> Al(OH)4^-}$$

The magnesium ion will react with the hydroxide ion in the sodium hydroxide solution to form magnesium hydroxide which is white. So, you see white precipitate.

$$\ce{Mg^2+ +2 OH^- -> Mg(OH)2}$$

However, in this case, it won't form any else by adding more sodium hydroxide. So, you will still see the white precipitate even though you have continued to add sodium hydroxide.

We can differentiate $\ce{Mg^2+}$ solution form the three solutions and now we are left with $\ce{Zn^2+}$ and $\ce{Al^3+}$. Take another sample from the remaining two solutions and add aqueous ammonia solution ($\ce{NH3}$) in the samples.

The zinc ion will react with the ammonia solution to form zinc hydroxide which is white. So, you see white precipitate.

$$\ce{Zn^2+ + 2NH3 + 2H2O <=> Zn(OH)2 + 2NH4^+}$$

Adding more ammonia solution, the zinc hydroxide will form tetraamminezinc(II) ion which is colourless. So, you will see a clear solution.

$$\ce{Zn(OH)2 + 4NH3 -> [Zn(NH3)4]^2+ + 2OH^-}$$

The aluminium ion will react with the ammonia solution to form aluminium hydroxide which is white. So, you see white precipitate.

$$\ce{Al^3+ + 3NH3 + 3H2O <=> Al(OH)3 + 3NH4^+}$$

However, the aluminium hydroxide will not further react with ammonia. So, you will still see the white precipitate even though you have continued to add ammonia.

In conclusion, first put sodium hydroxide in the three solutions (sample in test tube) and keep adding it until only one of the solutions still has white precipitate. That solution is $\ce{Mg^2+}$. Next, take the remaining two solutions (sample in test tube) and keep adding it until one of the solution still has white precipitate. That solution is $\ce{Al^3+}$. And finally the last solution is $\ce{Zn^2+}$.

syntax - An i-adjective immediately before 「ください」?

Does it make sense to have an i-adjective (in て-form) immediately before 「ください」?

For example, when asked to choose between hot and cold coffee, can I use 「温かくてください」, or must I turn it into nominal phrase (温かいのをください)?

Another example, is it fine to say 「優しくてください」, or must I insert a て-verb before ください (優しくしてください)?

Answer

In Japanese, you always need a main verb to complete a sentence. If you directly attach an i-adjective to an auxiliary ください via て, then you will not have a main verb anywhere. You need at least one main verb in between:

温かくしてください
優しくしてください

In sentences with i-adjectives or copula, it may not be obvious that you are using a verb, but underlyingly, you do have a verb. For example, the ordinary ending of an i-adjective is い:

寒い

This い includes a hidden verb ある, which is not obvious because the sequence くある is contracted to い. If you place something that interrupts the whole hidden sequence, thereby preventing the contraction, then you can see that there is indeed a hidden ある:

　部屋は暗いだけでなく、寒くもある。
× 部屋は暗いだけでなく、寒くもい。
× 部屋は暗いだけでなく、寒いも。

With nouns or na-adjectives, you may end a sentence with だ, but that is a contracted form of である, which includes the verb ある. Again, it may not be obvious that だ is the contracted form of である, but if you place something that interrupts the whole hidden sequence and prevents the contraction, you can see that there is indeed a hidden ある:

　彼は生徒でもある
× 彼は生徒もだ
× 彼は生徒だも

What kind of filter is that? Is it IIR?

I am trying to answer the following question:

Is the system described by equation:

$$y[n]=0.5y[n-1]+x[n]-0.5x[n-1]$$

an IIR filter? My answer is yes.

Thank you

Answer

This is the FIR filter, although it looks like an IIR. If you calculate the coefficients you get finite impulse response:

$h=[1]$

This happens due to zero-pole cancellation:

$Y(z)-0.5Y(z)z^{-1}=X(z)-0.5X(z)z^{-1}$

$H(z)=\dfrac{Y(z)}{X(z)}=\dfrac{1-0.5z^{-1}}{1-0.5z^{-1}}=1 $

Yes, it can be tricky. Seeing $y[n-k]$ coefficients in LCCDE (Linear Constant Coefficients Difference Equation) doesn't necessarily mean it's an IIR filter. It might be just a recursive FIR filter.

inorganic chemistry - Is KHF2 an ionic compound or a covalent compound?

The statement below is an excerpt from my school textbook:-

Because of the tendency of fluorine to form hydrogen bond, metal fluorides are solvated by $\ce{HF}$ giving species of the type $\ce{HF2-}$ like in $\ce{KHF2(KF.HF)}$. Also, because of hydrogen bonding, $\ce{HF}$ dimerises to $\ce{H2F2}$ and exhibits dibasic nature and forms acid salt like $\ce{KHF2}$ on reacting with $\ce{KOH}$ whereas $\ce{KHCl2}$ does not exist because chlorine does not form hydrogen bond.

But since $\ce{K+}$ is a cation and $\ce{HF2-}$ is an anion, it can easily form the ionic bond $\ce{K+HF2-}$. So, is KHF2 an ionic compound $\ce{K+HF2-}$ or a covalent compound $\ce{KHF2(KF.HF)}$?

Answer

I found this question very intriguing and while I support both answers by Ivan and Mithoron, I would like to add a little more insight.

When we consider compounds, we often tend to describe them as ionic or covalent. And often we can find both of these types in quite common molecules. We use these terms quite liberal, and when we talk about an ionic bond we usually mean a bond, that has predominantly ionic character, while a covalent bond has a predominantly covalent character.
Even in simple binary salts like sodium chloride we will not find the ideal ionic bond, and even methane the bond is not purely covalent. The truth - as always - lies somewhere in between.

What does that mean for potassium bifluoride? In this case it is especially difficult to classify the compound. This is less due to the potassium fluoride interaction, but to the interactions within the bifluoride subunit.
From the crystal structure itself one can clearly see, that there are not $\ce{KHF2}$ molecular units crystallising, but bifluoride ions in a lattice of potassium ions. The crystal structure itself is describes as follows.^[1]

It may be regarded as an ammonium chloride arrangement of potassium atoms and fluorine dumb-bells.

This clearly speaks to the predominantly ionic nature of the potassium fluorine bond. To gain further insight into the topic I ran a couple of quantum chemical calculations.^[2] Unfortunately I was unable to find a file with the crystal structure to run calculations on and I did not have the time to accurately reconstruct it from the parameters. Instead I would like to demonstrate on the example of $\ce{KF}$ how an (predominantly) ionic bond looks in the representation of the quantum theory in atoms in molecules (QTAIM).^[3] The electron density at the bond critical point is very low with $\rho(\text{BCP})=0.053~\mathrm{e\, a.\!u.^{-3}}$ and the second derivative at this point is positive, $\nabla^2\rho(\text{BCP})=+0.288~\mathrm{e\, a.\!u.^{-3}}$.

These are criteria which we use to characterise a mostly ionic bond. The compound $\ce{KF}$ can be regarded as (one of) the most ionic compound,^[4] so we can compare these values with values of other compounds.

Let's look at a covalent bond, before we look at the bifluoride ion. In this example I chose $\ce{HF}$ as it is related to it. Here we find a completely different picture. The electron density at the bond critical point is a lot larger, $\rho(\text{BCP})=0.366~\mathrm{e\, a.\!u.^{-3}}$ and the second derivative at this point is negative, $\nabla^2\rho(\text{BCP})=-2.858~\mathrm{e\, a.\!u.^{-3}}$. In the graphic one can see that there is charge accumulation along the bond path. All these criteria suggest, that this is a predominantly covalent bond.

When we do now look at the bifluoride ion, $\ce{[F-H-F]^-}$, we will see some intermediate bond, where it is hard to tell, which character is predominant. Note that due to symmetry reasons, we only need to look at one bond critical point. On the one hand we have a somewhat high electron density $\rho(\text{BCP})=0.177~\mathrm{e\, a.\!u.^{-3}}$ and the second derivative at this point is still significantly negative, $\nabla^2\rho(\text{BCP})=-0.416~\mathrm{e\, a.\!u.^{-3}}$. On the other hand we also see that the charge accumulation is not constant between the bonding partners, it is separated by an area where the Laplacian becomes positive, which indicates some ionic character.

So in this case it is quite hard to tell if we are talking about a covalent bond with high ionic character or an ionic bond with high covalent character. But to be perfectly honest here, this is the case with many hydrogen bonds.

I expect that these findings are comparable to the alkali metal bifluorides, which are all known up to at least caesium.^[5]

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Notes and References

1. Richard M. Bozorth, J. Am. Chem. Soc. 1923, 45 (9), pp 2128–2132.



2. Gaussian 09 Rev. D1; DF-BP86/def2-TZVPP; AIMAll 13.11.04;


3. The depicted QTAIM plots are the Laplacian distribution within the molecule. Solid blue lines indicate charge depletion $∇^2ρ>0$, dashed red lines indicate charge accumulation $∇^2ρ<0$, red spheres are bond critical points, solid black lines are bond paths, dark red lines are zero flux surfaces (these separate the atoms).


4. Why is KF the most ionic compound? (Chemistry.se)


5. R. Kruh, Keiichiro Fuwa, T. E. McEver, J. Am. Chem. Soc. 1956, 78 (17), pp 4256–4258.

purim torah in jest - PTIJ: Love Shalom and Kill Shalom?

The mishna says in pirkei avos:

הוי מתלמידיו של אהרן, אוהב שלום ורודף שלום

We should be like the students of Ahron - we should love Shalom, and chase to kill Shalom.

How is this possible in practice? The minute someone sees you being rodef shalom they'll either injury you or kill you! Furthermore, how is it possible to love shalom but also want to kill shalom? How can I do both at the same time?

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Answer

Aharon, as the first Kohen, was the quintessential representative of what it means to be a Kohen.

We see (Bamidbar 25:11-12) that Pinchas was awarded with becoming a Kohen for being קנא את קנאתי - taking up My (Hashem's) zealotry. So Kehuna fits with taking up Hashem's zealotry. As the prime alpha Kohen, Aharon certainly had this attribute.

Aharon chased Shalom even though he loved Shalom. Had he despised Shalom, then he wouldn't have been chasing Shalom for Hashem's zealotry - it would have been his own. It is only by loving Shalom that you can then chase him and be fulfilling the lofty level of taking up Hashem's zealotry.

Alternatively, it refers to chasing Shalom in the race for more reputation points. You should love him for all his contributions to the site, and chase after him in pursuit of more repuation. Gershon Gold is the only known violator of this precept.

gezel stealing - Switching movies in a Movie Theater

Are there any sources that would constitute the following as gezel/stealing: If you purchase a movie ticket to let’s say Spider-Man and you go to watch Spongebob, and both movie tickets are the same price?

bond - ATP break down and energy release?

I have a very basic question. Energy is absorbed to break bonds. Bond-breaking is an endothermic process. Energy is released when new bonds form. Bond-making is an exothermic process.

But ATP breaks down to ADP and releases energy right? Is there anything wrong in my understanding?

Answer

Bonds are formed between water and phosphate. Here is a good link:

Bonds are both broken and made in chemical reactions but many biology teachers and textbooks state that "Breaking ATP bonds releases energy." In reactions bonds are broken and made. If the strength of the bonds formed is exceeded by the strength of the bonds broken the reaction is exothermic.

halacha - Can a Gentile shovel / plow snow from your driveway on Shabbat if he has been paid for general work?

I read in Kitzur Shulcah Aruch (סימן צ - דין עשית חפציו בלא מלאכה ומלאכה על ידי גוי) that even if a person prepays a Gentile before Shabbat, he cannot tell him to specifically do work for him specifically on Shabbat. There is a rule that a Gentile cannot do work specifically for you without having some benefit for himself.

Let's say you tell the Gentile, "I am paying you a flat fee for the winter season. Whenever there is a lot of snow, I want you to shovel or plow my driveway." It snows on Shabbat. Can the Gentile shovel or plow your driveway in this situation? He gains no personal benefit from shovelling the snow, but, in this case, you did not specifically say that he must come and work on Shabbat, either. He showed up because it happened to snow that day.

mesorah tradition - what is the source for the artscroll sidur?

what is the mesorah for the artscoll ashkenaz siddur? Is this the same nusach ashkenaz that was used in previous generations?

Is using a parent's hidden object stealing?

Let’s say a mom has food hidden in her makeup kit in her bedroom and her son finds it and eats it. I’ve heard somewhere that kids are allowed to use various things in the home of their parents. So, if the mom didn’t directly say “don’t eat this food”, would sources consider this stealing? Also would the son allowed to share the food with his friends, or would this be stealing?

history - Origins of איל משולש and Vilna Ga'on's bathroom math

There is a well-known fact that the Vilna Ga'on studied math while in the bathroom since Torah was out of the question in an unclean place. It is also somewhat well-known that he produced the material for a book on geometry/הנדסה(?) during his time in the bathroom called איל משולש.

There is (or at least was in 1993) some speculation over the verity of these facts, as evidenced by the discussions on Mail Jewish here, here, and here, but my question specifically concerns the book and its origins.

According to the book's introduction, written by the compiler and editor Sh'mu'el ben Yosef from Loknik(?), the book is a collection of the Vilna Ga'on's notes. There is no indication that he did or did not intend them for publication.

1. Is anything known about the man who actually published the book and what his intentions were?


2. Was it supposed to simply exhibit the genius of the Vilna Ga'on?


3. Was it intended as a guide to students of math?


4. Students of math and Torah, perhaps?


5. Is there information in it that pertains to Torah at all?


6. Does it have value to the modern Torah- or math-learning audience?


7. Finally, how is the title pronounced?

Answer

Okay, I'll address part of part ("Does it have value to the modern... math-learning audience?") of question 6, and part of question 5, for now.

I've read chapter 1 only (and the main text only, not the marginal notes) so far, and it has definitions, postulates, and theorems from elementary plane geometry, lumping postulates and theorems together (i.e., not caring which are which; indeed, not dealing at all with the fact that some things are definitions and some are postulates and some are theorems). For example, the wider angle of a triangle is opposite the longer side; a quadrilateral with parallel opposite sides has equal opposite sides; etc. (The only misstatement AFAICT in that chapter, in #25, is that if an angle and two sides of one triangle equal an angle and two sides of another triangle, then the remaining angles and side of the triangles are also equal.) This is a reasonable basic-high-school-geometry text, I suppose, but not the way high school geometry is taught nowadays (where a lot of attention is paid to the difference between postulates and theorems, and to proofs). It may also be of some interest to students of the history of mathematics (I don't know), but not to mathematicians.

I'll bl"n get to the remaining chapters (and perhaps the introductions) at a later date.

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A later date:

I've now read chapter 2. Most of it deals with proportions. He discusses how if you add the first to the second term in a proportion, and add the third to the fourth, the result is still a valid proportion, and other such manipulations: rather more manipulations than I would have expected (he adds the first to the second, subtracts it, adds the second to the first, subtracts it, etc., etc.), but nothing that's not covered — though some of them as exercises — in a prealgebra class (or so). The last two paragraphs are on another topic: they state, first, that if you do the same thing to both sides of an equation then the result is still a valid equation, and, second, that if a=b and b=c then a=c. Again, this is covered in prealgebra (or so). Nothing of interest to mathematicians here.

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An even later date:

I've now read chapter 3. It deals with several topics, all of which seem to be therein order to build up to its two main results, the formula for the area of a circle and the Pythagorean theorem. Along the way he mentions and proves various results from high-school geometry, including that a triangle with two (or three) equal sides (or angles) has two (or three) equal angles (or sides), that corresponding angles formed by two parallel lines with a common transversal are equal, that the area of a triangle is half the base times the altitude, and the like. His two proofs of the Pythagorean theorem are standard, including Euclid's. He proves also that the circumference of a circle is more than three times its diameter, using a proof I haven't seen before, personally, but strongly suspect is well known. Finally, he proves that the area of a circle is half its circumference times its radius, using a method of proof that is by far not rigorous enough for a modern mathematician, but which approximates a standard proof from calculus: take concentric infinitesimal shells and sum their infinitesimal area. Again, there is nothing here that won't be found in many other places (except perhaps his proof that the circumference of a circle is more than three times its diameter, but, again, I doubt it).

Also, re question 5: In the first three chapters, there's no Torah content.

nuances - ズボン pronunciation variation & explanation for

I've heard it pronounced both low_high and high_low. Can anyone explain the meaning/reason behind the variation? (ie. difference in nuance, formal/casual, regional dialect, etc.) Ideally, I'd like to focus on one pronunciation to learn as a "standard" or "preferred learning pronunciation" if such a thing exists. よろしくお願いします！

Answer

ズボン is one of the words that is pronounced differently depending on the speaker. Typically it's pronounced as ズボン【HLL】, but elder people tend to prefer ズボン【LHL】. Both pronunciations are widely accepted. If you want to learn only one, I personally recommend ズボン【HLL】.

(Source: 『NHK日本語発音アクセント辞典』改訂 調査結果にもとづく作業方針の検討)

minhag - Modern nations and Umos Haolam

Where can I find a discussion about the roots of modern nations, in the Umos Haolam mentioned in the Torah and Chazal?

hashkafah philosophy - Does God's providence extend to all people or only righteous people?

Does God's providence (Hashgacha Pratit) extend to all people? to all individuals of the nation of Israel? or only to righteous people (צדיקים)?

Why does sodium sulfate have an unusual solubility-temperature curve?

For many salts there are solubility curves as a function of temperature that are smooth (don't have any kinks). Sodium sulfate, however, has a kink in the solubility-T curve at 30 degrees as shown below:

What happens when the temperature is about 30 degree?

everyday chemistry - Is the colour of leaves due to d-d transitions in chlorophyll?

While reading a chapter on transition metals, I came to know that d-Block elements have colour compounds due to d-d transitions. A question came to my mind as to whether there is any d-d kind of transitions in plants as they also show characteristics colours.

I know the green colours of leaves is due to presence of chlorophyll and also there are coloured pigments in plants.

I may be wrong in my thought, but I really want to clarify my doubt.

Answer

Let's rephrase your hypothesis and test it:

The green colour of leaves results from a d-d transition of the central atom of metal complexes known as chlorophylls.

Green leaves contain two types of chlorophyll, Chl a and Chl b, both have $\ce{Mg}$ as the central atom and show two distinct bands in the UV-VIS absorption spectrum.

The stronger ($\epsilon \approx 100000\, \mathrm{cm}^{-1}\cdot \mathrm{M}^{-1}$) band in the 400 nm (blue) region is known as the Soret band, the weaker $\epsilon \approx 30000\, \mathrm{cm}^{-1}\cdot \mathrm{M}^{-1}$) in the 660 nm (red) region is known as the Q band.

Now imagine that Chl a is treated with weak $\ce{HCl}$. In the resulting product, known as Pheophytin a, the central atom ($\ce{Mg^{2+}}$) is replaced with two protons.

In the UV-VIS absorption spectrum, however, we would still observe the two bands. They are slightly shifted and show somewhat different extinction coefficients, but the pattern is fundamentally the same.

We may conclude that our initial hypothesis is wrong. If it is not the absorption of the central atom in our complex, the ligand must be responsible.

Our new working hypothesis therefore is:

The colour of green leaves results from the absorption of the polycyclic pheophytin ligand and its extended $\pi$ system.

Let's simplify the Pheophytin a molecule: Removal of the E ring and replacing all the fancy substituents with ethyl groups leads to octaethylporphyrin as the core structure.

In the UV-VIS spectrum, we would still be able to see the strong Soret band, which corresponds to a $\pi,\pi^*$ transition from the ground state to the second excited singlet state ($S_0 \rightarrow S_2$).

halacha - Is there a purchasable copy of the Shulchan Aruch in Hebrew and English?

I'm looking to buy an actual Shulchan Aruch, not a Kitzur. I already own the Artscroll Kitzur and, while it is an amazing work, doesn't help very much when I want to research the actual halacha, where it comes from, and how it applies to a Sefard like myself. Is there an edition out there which is the whole original Shulchan Aruch by Yosef Karo in Hebrew and English?

Answer

Some partial English translation are available, see here:

http://www.jtsa.edu/x1212.xml#english_translations

But to answer your question, no there is no purchasable Hebrew/English Shulchan Aruch available. (If you just need Orach Chayim, the English translation of the Mishneh Berurah might suffice, although of course it lacks all of the other commentaries)

z transform - Derive the Forward Euler substitution for transfer function

In the book "The control handbook. Volume 1 " by Levine, the author shows that the transfer function:

can be aproximated and discretized in the transfer function:

using the forwar euler integral aproximation. In this way Levine shows that if i have a transfer function $G(s)=\frac{1}{s}$ i can simply substitute $s=\frac{z-1}{T}$ to apply the Forward Euler aproximation. At this point the author doesn't show how to generalize this particular case to a generic transfer function $H(s)$. Are you able to show me ?

Answer

To the extent you can factor the transfer function into individual integrator sections of the general form $\frac{1}{s}$ you can make this substitution, which is an approximation of the Matched-$z$ Transform where you substitute every $s$ for $s=\frac{\ln(z)}{T}$. (map from $s$ to $z$ using $z =e^{sT}$).

This results in first order forms given by $H_\mathrm{a}(s) = k_\mathrm{a}\frac{s-b}{s-a}$ being replaced with $H_\mathrm{d}(z) = k_\mathrm{d}\frac{z-e^{bT}}{z-e^{aT}}$ where $k_\mathrm{a}$ and $k_\mathrm{d}$ are fixed gain constants. $k_\mathrm{d}$ can be determined by using $H_\mathrm{a}(s=0) = H_\mathrm{d}(z=1)$ for low-pass forms or $H_\mathrm{a}(s=j \pi/T ) = H_\mathrm{d}(z=\pi)$ for high-pass forms.

For all pole forms this is also equivalent to what you would get using the mapping from $s$ to $z$ using the method of Impulse Invariance. The Matched-$z$ Transform is not recommended for higher order polynomials with zeros and poles since neither the time or frequency domain response is preserved (The method of Impulse Invarance or Bilinear Transform would more often be used, each with their own advantages).

This post summarizes various mapping techniques further: Are there alternatives to the bilinear transform?

When can you use the の particle to replace a noun?

How come the sentence 白いのは、高い is ok, but the sentence 学生じゃないのは、学校に行かない is not? Wouldn't the second sentence just mean "the one who isn't a student does not go to school"? On Tae Kim's grammar guide, he says that to replace a noun with の, the sentence needs to be "about the clause and not about the noun that was replaced." I'm not really sure what that means, so can someone please explain it?

minhag - Do some communities still allow more mingling between the sexes on Tu B'Av?

Do some communities still allow more mingling between the sexes on Tu B'Av? I understand that this used to be a custom, in addition to allowance of a more relaxed approach to women's tznius on that day (suggested by the article in the link). Do these customs still exist at all? If so, where, and to what extent?

halacha - Do black hats make the Jew?

It seems that wearing a hat is required, because the Shulchan Aruch says you need to wear a double covering. But some apparently-frum men don't wear a hat. How is this possible?

words - What is the difference between 語{かた}る and 話{はな}す?

What is the difference between 語{かた}る and 話{はな}す?

I know that I can say #1, but it's correct to say #2? If it's ok, sentence 1 and 2 have the same meaning?

1.私{わたし}は日本語{にほんご}を話{はな}す。

2.私{わたし}は日本語{にほんご}を語{かた}る。

Answer

私は日本語を話す。 I speak Japanese.

私は日本語を語る。 I talk about Japanese.

Since 語る has no special meaning associated with languages, it only means that you are talking what you know or how you feel about Japanese. It's quite popular in Japan to give the title ～を語る to books that celebrities reveal something or specialists express their thoughts.

Though I translated 日本語を話す into "speak Japanese", the verb doesn't have "be able to speak" sense, so every time you have to explicitly use potential form when you question about ability.

日本語が話せますか？ Do you speak Japanese?

compared to:

日本語を話しますか？ Are you going to speak Japanese?

A Japanese thesaurus has a neat summary including the difference of 話す and 語る. It's a shame that this forum has no ways to render tables.

          ... loudly  ... a perceptive  ... English    ... one's    ... oh! (a yell
                           comment                       past         of surprise)
言う          ○              ○             ×            ×              ○
しゃべる      ○              △             ○            △              ×

語る          ○              △             ×            ○              ×
話す          ○              △             ○            ○              ×
述べる        ○              ○             ×            ×              ×

organic chemistry - Need an explanation for how they got this compound name out of this structure

My professor posted this question as practice in naming compounds and provided the answer. I have stared at this for 30 minutes and cannot seem to figure out how he got this name out of it... Can someone please explain.

hashkafah philosophy - Intrinsic Value of Mitzvot

The question is the following: do mitzvot have intrinsic value, or only extrinsic value. A ramification of this is the following scenario: A person has two ways of performing an act; one of them would fulfill an optional mitzvah (see below), while the other, for technical reasons, would not. Assuming (in this thought experiment) that the positive effects of mitzvos (e.g. improving one's character traits and improving society) would be identically achieved with both acts, is there any advantage performing the act that fulfills a mitzvah.

The question comes down to whether there is intrinsic value to the mitzvot.

A corollary of this question is whether one receives divine reward for the mitzvos themselves, or only for the resultant benefits (e.g. self perfection).

What are the views of the Rishonim (medieval Jews) on the matter.

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Note: I am not asking whether there is extrinsic value to the mitzvot; i.e. ta'amei hamitzvot. I am asking if there is only extrinsic value in the mitzvot. I am also not looking for the views of the Zohar. Furthermore, I am aware that one who violates a negative commandment, or neglects a positive commandment faces punishment. This would certainly be a reason to perform them. However, this is not "intrinsic value". Thus, the practical relevance of the question is to mitzvot kiyumiot (optional mitzvot).

organic chemistry - Torquoselectivity: Disrotatory ring opening

In organic chemistry lecture we discussed the beginning of the Woodward Hoffmann Rules with a key step of the vitamin B12 synthesis.

(The initial paper from their work can be found here: http://pubs.acs.org/doi/pdf/10.1021/ja01080a054)

Let's first see the forward reaction (the electrocyclic ring closure) as Woodward and Hoffmann found (which goes by disrotatory cyclization; 6 electrons, thermal).

I'm interested in the reverse reaction, the ring opening (6 electrons, and therefore disrotatory:

I'm thinking now about the torquoselectivity of the ring-opening (because in an exercise we had an example with 1-Ethyl-1-ethoxy(EDG)-cyclobut-2-ene).

Is there a rule how to see why the E (E: Electron withdrawing group) is in trans position when I start with the product?

---

EDIT:

I'm thinking if they are some stereoelectronic effects here which explain the obtained selectivity:

See also: http://pubs.acs.org/doi/abs/10.1021/jo00244a058 (Electronic control of the stereoselectivities of electrocyclic reactions of cyclobutenes against incredible steric odds)

Well here we have a conrotatory ring-opening. I don't know if they are still valid in our 6e case for disrotatory ring-opening of the reaction from W. and H..

Answer

No, there is no general orbital symmetry rule for predicting which of the two possible disrotatory motions will be favored. However, by examining steric effects in the two possible transition states we can often make a good guess as to which product will predominate. There are always a few "special cases" like the one you referenced in your post, where with certain substituents under certain conditions certain things will happen. But to my knowledge there is no general rule for this situation.

In the following diagram there are 3 thermal reactions controlled by orbital symmetry (6 pi electrons, therefore disrotatory motion).

The top line shows the symmetry allowed disrotatory closure of trans, trans-1,6-dimethylhexatriene. There are two possible disrotatory motions - either the tops or the bottoms of the p-orbitals on carbons 1 and 6 can move towards each other in a disrotatory fashion. One motion produces the dimethylcyclohexadiene with the two methyl groups above the plane of the screen, the other motion produces the mirror image molecule with the methyl groups below the plane of the screen.

Similarly, cis, cis-1,6-dimethylhexatriene can undergo two disrotatory motions to produce the same two products (Note: the cis, cis isomer will react much slower and probably in lower yield; steric interactions between the methyl groups will disfavor the s-trans conformation about the two single bonds that is required for the ring closure to be able to occur).

The bottom line shows the reverse reaction, thermally converting a cyclohexadiene to a hexatriene. As shown, two possible isomers can be formed. The ratio of these two isomers will depend on steric interactions that develop during the two possible disrotatory motions. In this case, we will primarily obtain the trans, trans isomer; the cis, cis isomer has steric problems in its transition state from the two methyl groups bumping into each other (build a model).

In this last reaction, if we replaced the methyl groups with deuterium, we would obtain a roughly equal mixture of the two possible products, cis, cis- and trans, trans-1,6-dideuteriohexatriene. So again, there is no orbital symmetry "rule" for predicting whether a group would wind up cis or trans on the double bond. But if we examine the steric effects in the two possible disrotatory transition states, we can often make a good guess about which isomer should predominate.

talmud yerushalmi - Were all future Torah innovations taught to Moshe at Har Sinai?

Pirkei D'Rabbi Eliezer Ch. 2-------פרקי דרבי אליעזר פרק ב

אמר לו, (רבי יוחנן לרבי אליעזר) אמשול לך משל למה הדבר דומה, למעין זה שהוא נובע ומוציא מים, ויש בכוחו להוציא מים יותר ממה שהוא מכניס. כך אתה יכול לומר דברי תורה יותר ממה שקבלו מסיני.

[Translation by Seferia]: (R. Yochanan) said to him (R' Eliezer), I will (also) tell thee a parable. To what is the matter like? To this fountain which is bubbling and sending forth its water, and it is able to effect a discharge more powerful than what it secretes; in like manner you are able to speak words of the Torah in excess of what Moses received at Sinai.

How can this be reconciled with:

Talmud Yerushalmi (Peah 2:4 - page 13a):---תלמוד ירושלמי פרק ב הלכה ד - דף יג עמוד א

ריב"ל אמר... אפי' מה שתלמיד ותיק עתיד להורות לפני רבו כבר נאמר למשה בסיני מה טעם (קוהלת א) יש דבר שיאמר אדם ראה זה חדש הוא וגו' משיבו חבירו ואומר לו כבר היה לעולמים

R, Yehoshua Ben Levi says... Even that which a senior student will lecture in front of his master, was already said to Moshe at Sinai. What is the reason (source) of this? [From the passuk: (Koheles 1:10) Sometimes there is a phenomenon of which one might say say, “Look, this one is new!”— And his friend will respond and say to him "it occurred long since, in ages that went by before":

Summary: In the Pirkei D'Rabbi Eliezer R' Yochanan tells R' Eliezer that he is able to speak words of the Torah in excess of what was received at Sinai. The Yerushalmi says that everything taught by students in foront of their masters was already said to Moshe at Sinai?

Suggested reconciliation:

The words in the Pirkei D'Rabbi Eliezer read: "יותר ממה שקבלו מסיני" more than they received at Sinai, which may be understood to mean that which the B'nei Yisrael learned at Sinai. And the Yerushhalmi says "נאמר למשה בסיני" was said to Moshe at Sinai, so it may not be a contradiction, because Maybe Moshe was taught everything, but not B'nei Yisrael, and R' Eliezer taught that which had not been learned by B'nai Yisrael at Sinai.

But, see Orchos Tzadikim - Ways of the Righteous, Sha'ar Hatorah which cites the Pirkei D'Rabbi Eliezer, and he says "

וכן מצינו ברבי אליעזר הגדול: מתוך שעסק בתורה הרבה, העידו עליו רבותינו זכרונם לברכה שנתגלה לו מה שלא נתגלה למשה מסיני

So we find with R' Eliezer the Great: since he studied much Torah our Rabbis testified that it was revealed to him even that which was not revealed to Moshe at Sainai".

So according to the understanding of The Orchos Tzadikim R' Eliezer taught words of Torah in excess of even what Moshe received at Sinai. Thus we are back to our question of how to reconcile Pirkei D'Rabbi Eliezer with the Yerushalmi.

Answer

This is addressed by R. David Luria in his commentary to the statement in Pirkei D'Rabbi Eliezer. He notes that it appears to be contradictory to the statement about all future Torah being already said to Moshe at Sinai. He states that this is resolved with the textual emendation attributed to R. Elija of Vilna, which replaces the words "שקיבלו מסיני" with "שקיבל ממני", in which case R. Yochanan Ben Zakai was referring to himself, not to Moshe.

In your edit you note that the Orchos Tzadikim has a version of the text which clearly states "that was not revealed to Moshe at Sinai", and thus the question remains how the author would address the above contradiction. This too is addressed by R. David Luria, and he suggests that R. Yochanan Ben Zakai was specifically referring to the reasons for the Red Heifer, which is already established by other midrashim as something that was revealed to R. Eliezer and not Moshe.

כגירסא זו נראה שהיה גם כן לפני באל ארחות צדיקים שכתב בשער התורה וז"ל וכן מצאנו לר"א הגדול כו' העיגו עליו רבותיו שנתגלה לו יותר ממה שנתגלו למשה בסיני עכ"ל וי"ל לגירסא זו שנתכוון רבי יוחנן בן זכאי לרמוז על טעמי פרה שלא נתגלו למשה ונתגלו לר"א וכמ"ש ברבה חוקת ובפסיקתא פרה הבאתים לעיל פ"א אות כ"ח ובשם האחד אליעזר ע"ש ובהגהות המיוחסות להגר"א גרס שקיבל ממני ור"ל מן רבי יוחנן בן זכאי נראה שלא הונח לו ז"ל לגרוס יותר ממה שקיבלו מסיני שהרי אמרו בויקרא רבה ר"פ כ"ב וקהלת רבה פ"א ופ"ה שאפילו מה שתלמיד ותיק עתיד לומר לפני רבו כלן נאמרו למשה בסיני שנאמר יש דבר שיאמרו זה חדש הוא כבר היה לעולמים

computational chemistry - Software for visualizing molecular force vectors

I would like to visualize molecular normal modes as vectors sitting on each atom, and not as actual vibrations. I am able to do this, in part, with Molden by copying in the vector into a file readable by Molden (extension is .geo.molden, and is generated from a Molcas calculation). The vector is represented as red lines, but they do not look very nice (see image). Also the background is black, and Molden has a limited number of ways to visualize the molecule.

Is there some other software (free) that can do this? Perhaps Avogadro, VMD, or something along these lines? Specifically I would like to be able to change to different molecular visualizations, and show the vectors as arrows with a easily distinguished color.

Figure 1. This is what Molden can do... not very pretty!

Or possibly, after changing the background color to white with GIMP:

Figure 2. Not really better, since the Hydrogen atoms are represented with white by Molden, as is the label text.

bond - Bonding in the phosphate ion

I'm looking for an explanation of the bonding in the phosphate (PO₄³⁻) ion:

(Image courtesy of Wikipedia)

Phosphorus (₁₅P) - being the fifteenth element - has fifteen electrons, five valence electrons and the following electron configuration:

1s²
2s² 2p⁶
3s² 3p³

This being so, by what means does it form its bonds? Naively, one might expect it to form 3 single covalent bonds and be happy. But it doesn't, it forms five bonds, presumably using each of its five electrons. My first question is - why would it do this? It seems to me that this would result in the Phosphorus atom having ten electrons in its outer shell (four from the double bond with the oxygen and two each from the single bonds with the other three oxygens).

Apart from the oxygen with a double-bond, we have three oxygens forming single bonds. Does this not leave them one electron short?

Finally, why are the oxygens shown as carrying a negative charge?

usage - Particles in the Passive form causing me confusion (を、に、が)

Sometimes, I dont know what particles to use in the passive form に、を、が。

ワインを飲まれた

ワインに飲まれた

ワインが飲まれた

I REALLY dont understand the difference between those three. Is the first one that uses を　indicating that there is a subject that drank the wine? Do all of them mean that the wine has been drunk?

Thanks!

Answer

We usually do not say 'ワインに飲まれた'. It would mean 'Something was drunk by wine'.

'ワインを飲まれた' sounds to me like 'Someone drank "my" wine'.

I think 'ワインが飲まれた' just means '(The) wine was drunk./Someone or some people drank (the) wine.' In this sentence the wine might not have been mine.

acid base - Why is HF the least acidic hydrogen halide?

Fluorine is the most electronegative halogen and therefore, there is larger difference in electronegativity between the atoms of $\ce{HF}$ than any other hydrogen halide, which means the positive charge on hydrogen atom is the greatest in this compound and hence a comparatively small negative charge is needed to attract it. If so, why is it classified as least acidic hydrogen halide if the $\ce{H+}$ is easy to remove?

Answer

First of all as @chipbuster says $\ce{HF}$ in diluted solutions in water is nearly completely dissociated and therefore shouldn't be called weak. Wikipedia describes this nicely and cites several sources for this claim.

It was rather difficult to prove (spectroscopic methods were used), because hydronium ions created in dissociation are mostly bound to fluorine anions with hydrogen bonds, in what is called tight ion pairs. It prevents from detecting the true strength of $\ce{HF}$ with methods like acid–base titration - they show dissociation of ionic pair. Similar effect is present in ion exchange resins.

Strength of this acid is revealed in more concentrated solutions, where $\ce{HF}$ molecules replace hydronium ions, creating bifluoride anions, freeing them - it's homoassotiation mentioned by Wildcat.

More to the point - does it mean that $\ce{HF}$ isn't weaker acid than other hydrogen halides? The answer isn't simple, and acidity itself depends on many factors.

In terms of $\ce{K_a}$ in diluted aqueous solutions $\ce{HF}$ is probably still weaker than $\ce{HCl}$ and the rest but getting exact value is greater problem than normally (generally values of $\ce{K_a}$ for strong acids aren't precise). Decrease in acidity between hydrogen halides is described in answer to this question

For concentrated solutions one needs to use Hammett $H_0$ function which gets lower than -10 in pure $\ce{HF}$ (pure sulfuric acid has -12) - it means it's very strong, although not superacidic.

See also:

The Hammett Acidity Function $H_0$ for Hydrofluoric Acid Solutions

history - Who composed the Piyut Echad Mi Yodeya?

Who composed the Piyut Echad Mi Yodeya that is commonly recited on Pesach?

Answer

Per Wikipedia the author is unknown.

discrete signals - GCC-PHAT (Generalized cross correlation MATLAB)

I've been trying to implement generalized cross correlation with a PHAT weighting function for a while now, and cannot get it to work. I have tried correlating using MATLAB's xcorr.m file, and it works for getting a correct delay tau (on simulated sinusoidal signals).

The code for the signals are thus:

Fs = 8000;
dt = 1/Fs;%0.125e-3
f1 = 100;
tdelay = 0.625e-03;%try different values
t3 = (0:dt:(1)-dt)';
x3 = cos(2*pi*f1*t3);
x4 = cos(2*pi*f1*(t3-tdelay));

As can be seen in part of the source code for xcorr.m, the cross correlation is implemented thus:

%Transform both vectors

X = fft(x,2^nextpow2(2*M-1));
Y = fft(y,2^nextpow2(2*M-1));

% Compute cross-correlation

c = ifft(X.*conj(Y));

According to definitions of GCC-PHAT, the only addition I needed to make was to divide the product by its own magnitude, before taking the ifft. Here is my version with this change.

%Transform both vectors
X = fft(x,2^nextpow2(2*M-1));
Y = fft(y,2^nextpow2(2*M-1));

% Compute cross-correlation

R = X.*conj(Y);
c = ifft(R./abs(R));

However I always end up with a tau of zero with the PHAT weighting! On closer examination of the array produced as a result of this division, it seems as if the first value of R is a real value (with no imaginary component), and so when divided by its magnitude it becomes 1. All the other values in array R are complex, so do not end up as 1 when divided by their own magnitude and so end up with a value of <1.

This can be seen below, for the 1st 10 values of R.

    K>> R(1:10,1)

ans =

  0.000000000000000 + 0.000000000000000i
 -0.494299608718696 - 0.003002230689022i
 -0.002678647083223 - 0.000032538742345i
 -0.488954228290329 - 0.008909374553649i
 -0.010656518992354 - 0.000258902698589i

 -0.478379290671260 - 0.014528074329782i
 -0.023760667475633 - 0.000865926459320i
 -0.462803929640386 - 0.019677623220519i
 -0.041707017319469 - 0.002026674993917i
 -0.442565618721743 - 0.024194329448597i

K>> abs(R(1:10,1))

ans =


   0.000000000000000
   0.494308725968464
   0.002678844707371
   0.489035391682370
   0.010659663580139
   0.478599844010494
   0.023776441018801
   0.463222070011989
   0.041756229537848
   0.443226457301486


K>> R(1:10,1)./abs(R(1:10,1))

ans =

  1.000000000000000 + 0.000000000000000i
 -0.999981555555690 - 0.006073594357736i
 -0.999926227844417 - 0.012146557900713i
 -0.999834033705084 - 0.018218261306199i
 -0.999705001216859 - 0.024288074069393i

 -0.999539169638280 - 0.030355367874845i
 -0.999336589392997 - 0.036419515378054i
 -0.999097322000240 - 0.042479891383435i
 -0.998821440083941 - 0.048535871565711i
 -0.998509027227826 - 0.054586834901284i

As can be seen above, the largest value ends up being at the 1st index, when we divide R by its own magnitude. So once the ifft is taken, the highest value is ALWAYS at the beginning of the array, which gives a lag and timediff of zero...even when I set the delay between the 2 identical signals at the beginning to a nonzero value (e.g. delay = 0.75e-03).

What am I doing wrong?? Any help appreciated.

Rory

P.S. if anyone is wondering why I'm bothering with the PHAT weighting, its because it should give far better results (in theory) in a real life scenario, for TDOA.

reference request - Good Introduction to chemistry textbook

I want to learn basic chemistry, so which textbook do you think I should pick? It should be something both concise and clear. Thank you.

hebrew - Correcting tav/sav

If someone who usually pronounces the letter "ת" without a dagesh as "sav" is leining Torah, and he accidentally says "tav" in a place where he would normally say "sav", should the gabbai correct him?

Does it make a difference whether the word with the "ת" replaced by a "ט" means something totally different? Perhaps that doesn't even make a difference at all because by saying "tav" instead of "sav," the leiner indicates that he thinks that the letter is different from what it actually is.

halacha - May we genetically engineer stuff?

The possibilities of genetic engineering continue to grow. May a Jewish scientist genetically engineer things?

Answer

Genetic engineering has been cited by some as both halachically acceptable and problematic in several respects:

• Stem Cell Research -- Unlike some other religions, Judaism does not define a fetus as a human being with full rights until after 40 days of gestation. Yevamos 69a; Nidda 30b. But see Rebbe's position at Sanhedrin 91a (holding that the soul is created at gestation). Accordingly, most poskim permit Jewish scientists to do research on embryo stem cells that are less than 40 days since gestation. Sources: RCA Statement and a lecture I heard from Rabbi Dr. Barry Fruendel.


• Cloning -- Research indicates that, subject to more safety improvements, it will be possible for a woman to take her own skin or bone-marrow cells and create a gamete-like cells with only 23 chromosomes that could be attached to the woman's own egg cell to create a perfect copy of herself. This could be a violation of the concept raised in Niddah 30 that there are three partners to the creation of a new soul, a man, a woman and Hashem. Cloning would appear to intentionally by-pass part of this Divine process. To my knowledge, this has only been studied by our sages from the perspective of unmarried women using in vitro fertilization to have children without having relations. But the decisions of Rabbi Shlomo Zalman Auerbach, zt'l, Nishmat Avraham, vol. 4, Even haezer 1:3, and Rav Moshe Feinstein, zt'l, cited in R.V. Grazi and J.B. Wolowelsky, “Parenthood from the Grave,” The Jewish Spectator 65:4 (Spring 2001, Aviv 5761), appear more concerned that the sperm donor might not be Jewish. So I am unaware of a precedential decision that is directly on point here.


• Transgenic Species -- Already we are seeing the use of DNA material from foreign species injected into the cellular structures of animals and plants to alter those species into what is called a transgenic species -- and also the enhancement of an animal's DNA with the DNA of other creatures of its species, a process called cisgenic. While cisgenic animals and plants are not problematic, the creation of transgenic species crosses into the area of kilayim. Leviticus 19:19 states: "You shall keep my statutes. You shall not let your animal mate with a different species; you shall not sow your field with different species of plants." Most sages appear to agree that, with respect to animals, the prohibition only applies to actual inter-breeding of mixed species. Taking the genetic material of different animal species and making transfers on the cellular level is generally accepted. Akiva Wolff, "Jewish Perspectives on Genetic Engineering," Jerusalem Center for Public Affairs (Oct. 2001). However, there are differing opinions about transgenic plant species. Id.


• Transgenic Animals With Human DNA -- Some scientists believe that research on brain diseases such as Alzheimer's and Parkinson's requires using stem cells to creating lab animals (apes in particular) with genetically human brains. Beyond the ethical considerations raised in the science fiction movie, Planet of the Apes, some commentators have suggested that the rabbis' current view that transgenic animals are not subject to kilayim should be reconsidered if their view is based on the assumption that the animals will be sterile. If they can be made to reproduce with human-type gonads, writes Leora Perlow and John D. Loike (separately), it may be possible that in a few generations the grandchildren of the original transgenic ape could mate with a human. Whereas the species of cross-bred animals was always decided by the mother of the animal (Bechoros 5b), what do we call the product of a transgenic advanced ape male and a human female? And what halachic status will the product have?

tanach - When are the prophets and the writings read

I understand the yearly Torah reading, but when is the rest of the Tanach read?. is there a schedule for the rest of the Tanach?

periodic - periodicity coefficient

I wonder if an efficient method exist to compute how much a signal is periodic, it should be ~1.0 when the signal is totally periodic (like a sinusoïdal signal) and ~0.0 when totally random, like a white noise.

Edit : This question came with a big misunderstanding, it has been modified to fit the answer.

Answer

I suggest using Spectral Flatness, aka Wiener Entropy. It is defined as a ratio of geometric and arithmetic mean of the magnitude spectra $X(k)$:

$$\Xi=\dfrac{\sqrt[k]{\prod_{k=0}^{K} X(k)}}{\frac{1}{K}\sum_{k=0}^{K}X(k)} $$

For signals which have flat spectra, its value tends towards $1$, whereas for tonal signals it is close to $0$. In your particular application, you might want to consider $1-\Xi$ as a measure of "tonalness" in your signal.

tefilla - Why are there musafos for sh'kalim and hachodesh, but not zachor or para

Why are there musafos (things added to the chazaras hashatz of musaf) for Shabas parashas sh'kalim and hachodesh but not zachor or para? (Or, at least, many nusach ashkenaz and nusach sefard sidurim, including Rav Yaakov Emden's, have the former but not the latter.)

Answer

See this article (Hebrew).

The piyutim (shivatot) classically recited by nusach Ashkenaz at musaf of shekalim and hachodesh (although now omitted by many, many congregations) were composed by the Kalir.

The author notes that the Kalir actually composed many shivatot for all of the arba parshiyot, but he claims that for some reason, only two (for shekalim and hachodesh) had arrived in Europe by the 11th century, where they were recited at musaf.

He proves this from the fact that R. Meir Shatz of Worms felt the need to compose shivatot (in the style of the Kalir) for the two missing shabbatot. However, reciting these shivatot never became accepted as mainstream minhag Ashkenaz.

What is even more surprising is that some of the Kalir's shivatot for zachor and parah did eventually make it into Ashkenaz in the 12th century (they appear in Ashkenazi manuscripts and are the subjects of Ashkenazi commentaries) but they were never adopted as part of minhag Ashkenaz.

Bottom line, the answer is that there are no piyutim recited at musaf of zachor and parah because the Kalir's piyutim were not available in Ashkenaz when minhag Ashkenaz was getting started, and later developments (R. Meir Shatz's composition or the subsequent arrival of the Kalir's piyutim) were not sufficient to change the status quo.

stereochemistry - Atropisomerism of naphthyl alcohol

In March's Advanced Organic Chemistry (6th ed.), it's stated that the above two are atropisomers. I don't get why is it so. How is the topmost $\ce{C}$ locked in its place? Surely, there's steric hindrance due to presence of two methyls but how does that prevent rotation? It can certainly rotate with the methyls being "rigid" in their positions. Also, are they chiral? I believe they aren't because they are superimposable mirror images.

halacha - Can vegetables/fruit be uncheckable?

There are differences in 'bug checking strategies' for different countries due to differences in bugs, pesticides, harvesting and packaging techniques (etc.). In Israel, I have recently encountered people who will not eat certain fruits or vegetables (strawberries, figs, cabbage, etc.) which they render 'uncheckable'. I was directed to the reputable kosharot website when trying to check a cabbage:

פוסקי הדור מציינים שבגלל כמה סיבות שונות אין לאדם רגיל (שאין לו הכשרה מיוחדת בבדיקת ירקות עלים) להשתמש בירקות עלים לא מפוקחים ומכונים בפי כל "ירקות גוש קטיף

The decisors of [halacha of this] generation mark that, for a number of different reasons, a regular person (who has no special preparation in checking leaf vegetables) is not to use leaf vegetables not supervised and nicknamed in everyone's speech "Gush Katif vegetables"

I found it strange that some vegetables are 'impossible' to be check for bugs, unless you are an expert. Certainly 'bug problems' now are no worse than the situations that our ancestors encountered. Why, nowadays, would some things be forbidden on the grounds that some bugs are impossible to be found/removed? Perhaps I am naive in thinking that all vegetables/fruits were eaten in the past as long as they were checked - perhaps they weren't, for this reason. If anyone can shed light on this it would be most appreciated.

(As an aside I went on a tiyul in Israel where our tour guide pointed out a hefker fig tree, picked a fig, opened it, spent time checking it and ate it. Another member of the tour said that his Rosh Yeshiva forbids eating figs because they cannot be checked. How is it possible that one of the shiv'at ha'minim are impossible to check and therefore inedible?!)

grammar dikduk - articulation of resh with dagesh

It is well known that ר not lend itself to gemination. It never has virtual gemination. As for the full gemination indicated by the dagesh, ר allows it, but only very rarely, and never after the definite article. There are only about 15 words in Tanakh e.g. in 1Sam 10:24. I wonder if there has been an old tradition of articulation of the resh. Is it possible that the name שָׂרָ֖ה has once been spelled Sarra (and not Sara)? The famous pasuk Gen 17:15 (וַיֹּ֤אמֶר אֱלֹהִים֙ אֶל־אַבְרָהָ֔ם שָׂרַ֣י אִשְׁתְּךָ֔ לֹא־תִקְרָ֥א אֶת־שְׁמָ֖הּ שָׂרָ֑י כִּ֥י שָׂרָ֖ה שְׁמָֽהּ) is translated by the Septuaginta as follows: εἶπεν δὲ ὁ θεὸς τῷ Αβρααμ Σαρα ἡ γυνή σου οὐ κληθήσεται τὸ ὄνομα αὐτῆς Σαρα ἀλλὰ Σαρρα ἔσται τὸ ὄνομα αὐτῆς . The Name Sara is transliterated Σαρρα and not Σαρα whereas Sarai is transliterated with Σαρα. Any ideas?

periodic table - What is the formula for finding the average atomic mass of an element based on the abundance of its isotopes?

In my class my teacher showed us how to find the average atomic mass of an element with a method, but he didn't really state a formula one could use. I came up with a formula of my own, and from what I observed it works: $$ \frac{i_1x + i_2y}{100} = A, $$ where $A$ is the atomic mass, $i_1$ is the first isotope's atomic weight, $i_2$ is the second isotope's atomic weight, $x$ and $y$ are the percentages of the isotopes, respectively, and they add up to 100, i.e. $x+y = 100$.

Therefore: $$ \frac{i_1x + i_2(100-x)}{100} = A $$

I'm just wondering, is there an official formula, or is this method it?

Answer

The average relative atomic mass of an element comprised of $n$ isotopes with relative atomic masses $A_i$ and relative fractional abundances $p_i$ is given by:

$$ A = p_1 A_1 + p_2 A_2 + \dots + p_n A_n = \sum\limits_{i=1}^n p_i A_i $$

For example carbon:

\begin{array}{lrrr} \text{Isotope} & \text{Isotopic Mass $A$} & \text{Abundance $p$} & A\times p\\\hline \ce{^{12}C}: & \pu{12.000000 u} & 0.98892 &= \pu{11.867 u}\\ \ce{^{13}C}: & \pu{13.003354 u} & 0.01108 &= \pu{00.144 u} \end{array}

Since we have $p_1A_1$ and $p_2A_2$, we add those together to find $A$, therefore the chemical relative atomic mass of carbon is $$A = \pu{00.144 u} + \pu{11.867 u} = \pu{12.0011 u}.$$

frequency - What is the physical significance of negative frequencies?

This has been one of the holes in my cheddar cheese block of understanding DSP, so what is the physical interpretation of having a negative frequency?

If you have a physical tone at some frequency and it is DFT'd, you get a result in both the positive and negative frequencies - why and how does this occur? What does it mean?

Edit: Oct 18th 2011. I have provided my own answer, but expanded the question to include the roots of why negative frequencies MUST exist.

Answer

This has turned out to be quite the hot topic.

After reading the rich multitude of good and diverse opinions and interpretations and letting the issue simmer in my head for sometime, I believe I have a physical interpretation of the phenomenon of negative frequencies. And I believe the key interpretation here is that fourier is blind to time. Expaning on this further:

There has been a lot of talk about the 'direction' of the frequency, and thus how it can be +ve or -ve. While the overarching insights of the authors saying this is not lost, this statement is nontheless inconsistent with the definition of temporal frequency, so first we must define our terms very carefully. For example:

• 
  

  Distance is a scalar (can only ever be +ve), while displacement is a vector. (ie, has direction, can be +ve or -ve to illustrate heading).

  
  


• 
  

  Speed is a scalar (can only be +ve), while velocity is a vector. (ie, again, has direction, and can be +ve or -ve).

  
  
  

Thus by the same tokens,

• Temporal Frequency is a scalar, (can only be +ve)! Frequency is defined as number of cycles per unit time. If this is the accepted definition, we cannot simply claim that it is going in 'a different direction'. Its a scalar after-all. Instead, we must define a new term - the vector equivalent of frequency. Perhaps 'angular frequency' would be the right terminology here, and indeed, that is precisely what a digital frequency measures.

Now all the sudden we are in the business of measuring number of rotations per unit time, (a vector quantity that can have direction), VS just the number of repititions of some physical oscillation.

Thus when we are asking about the physical interpretation of negative frequencies, we are also implicitly asking about how the scalar and very real measures of number of oscillations per unit time of some physical phenomenon like waves on a beach, sinusoidal AC current over a wire, map to this angular-frequency that now all the sudden happens to have direction, either clockwise or counterclockwise.

From here, to arrive at a physical interpretation of negative frequencies two facts need to be heeded. The first one is that as Fourier pointed out, an oscillatory real tone with scalar temporal frequency, f, can be constructed by adding two oscillatory complex tones, with vector angular frequencies, +w and -w together.

$$ \cos(\omega_0 t)=\frac{e^{\jmath \omega_0t}+e^{-\jmath \omega_0 t}}{2} $$

Thats great, but so what? Well, the complex tones are rotating in directions opposite to each other. (See also Sebastian's comment). But what is the significance of the 'directions' here that give our angular frequencies their vector status? What physical quantity is being reflected in the direction of rotation? The answer is time. In the first complex tone, time is travelling in the +ve direction, and in the second complex tone, time is travelling in the -ve direction. Time is going backwards.

Keeping this in mind and taking a quick diversion to recall that temporal frequency is the first derivative of phase with respect to time, (simply the change of phase over time), everything begins to fall into place:

The physical interpretation of negative frequencies is as follows:

My first realization was that fourier is time-agnostic. That is, if you think about it, there is nothing in fourier analysis or the transform itself that can tell you what the 'direction' of time is. Now, imagine a physically oscillating system (ie a real sinusoid from say, a current over a wire) that is oscillating at some scalar temporal-frequency, f.

Imagine 'looking' down this wave, in the forwards direction of time as it progresses. Now imagine calculating its difference in phase at every point in time you progress further. This will give you your scalar temporal frequency, and your frquency is positive. So far so good.

But wait a minute - if fourier is blind to time, then why should it only consider your wave in the 'forward' time direction? There is nothing special about that direction in time. Thus by symmetry, the other direction of time must also be considered. Thus now imagine 'looking' up at the same wave, (ie, backwards in time), and also performing the same delta-phase calculation. Since time is going backwards now, and your frequency is change-of-phase/(negative time), your frequency will now be negative!

What Fourier is really saying, is that this signal has energy if played forward in time at frequency bin f, but ALSO has energy if played backwards in time albeit at frequency bin -f. In a sense it MUST say this because fourier has no way of 'knowing' what the 'true' direction of time is!

So how does fourier capture this? Well, in order to show the direction of time, a rotation of some sort must be employed such that a clockwise roation dealinates 'looking' at the signal in the forward arrow of time, and a counterclockwise roation dealinates 'looking' at the signal as if time was going backwards. The scalar temporal frequency we are all familiar with should now be equal to the (scaled) absolute value of our vector angular frequency. But how can a point signifying the displacement of a sinusoid wave arrive at its starting point after one cycle yet simultaneously rotate around a circle and maintain a manifestation of the temporal frequency it signifies? Only if the major axes of that circle are composed of measuring displacement of this point relative to the original sinusoid, and a sinusoid off by 90 degrees. (This is exactly how fourier gets his sine and cosine bases the you project against every time you perform a DFT!). And finally, how do we keep those axes seperate? The 'j' guarantees that the magnitude on each axis is always independant of the magnitude on the other, since real and imaginary numbers cannot be added to yield a new number in either domain. (But this is just a side note).

Thus in summary:

The fourier transform is time-agnostic. It cannot tell the direction of time. This is at the heart of negative frequencies. Since frequency = phase-change/time, anytime you take the DFT of a signal, fourier is saying that if time was going forwards, your energy is located on the +ve frequency axis, but if your time was going backwards, your energy is located on the -ve frequency axis.

As our universe has shown before, it is precisely because Fourier does not know the direction of time, that both sides of the DFT must be symmetric, and why the existence of negative frequencies are necessary and in fact very real indeed.

Finding pH of tri-protic acid

I am studying for my final and I am given this problem:

A solution of sodium phosphate is made from 10.5 g sodium phosphate in 150 mL of water. What is the pH of this solution

Given: Ka1, Ka2.

The solution says that we can simply calculate this pH with the following eqution: $$pH=\frac{pK_{a1}+pK_{a2}}{2}$$ However this makes absolutely no sense to me, as this is the pH at the equivalence point. What am I missing as towhy this equation can be used?

Answer

A chemical species that behaves both as an acid and as a base is called amphoteric. This property depends upon the medium in which the species is investigated: $\ce{H2SO4}$ is an acid when studied in water, but becomes amphoteric in superacids.

from the IUPAC goldbook.

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For ampholytes like $\ce{NaH2PO4}$ the $\ce{pH}$ is independent on the concentration (in first approximation). Consider the reactions of that are possible: \begin{align}\ce{ H2A- + H3+O &~<=> H3A + H2O \tag1\\ H2A- + H2O &~<=> HA^{2-} + H3+O \tag2\\ HA^{2-} + H2O &~<=> A^{3-} + H3+O \tag3\\ }\end{align}

As the first approximation, we will assume that everything happening in equation $(3)$ is negligible, as is will only very little influence the concentration of $\ce{HA^{2-}}$. Therefore we can focus on the acidity constants $K_{a_1}$ of $(1)$ and $K_{a_2}$ of $(2)$: \begin{align} K_{a_1} &= \frac{c(\ce{H3+O})\cdot c(\ce{H2A-}) }{c(\ce{H3A})} \tag4\\ K_{a_2} &= \frac{c(\ce{H3+O})\cdot c(\ce{HA^{2-}})}{c(\ce{H2A-})} \tag5\\ \end{align} We will just go ahead and multiply these equations, since they are coupled, simultaneously happening processes. Then we will cancel whatever cancels. \begin{align} K_{a_1} \cdot K_{a_2} &= \frac{c(\ce{H3+O})\cdot c(\ce{H2A-}) }{c(\ce{H3A})} \cdot \frac{c(\ce{H3+O})\cdot c(\ce{HA^{2-}})}{c(\ce{H2A-})} \\ K_{a_1} \cdot K_{a_2} &= c^2(\ce{H3+O})\cdot \frac{c(\ce{HA^{2-}})}{c(\ce{H3A})} \tag7\\ \end{align} Now another major assumption is that the reactions $(1)$ and $(2)$ are happening to the same extent and therefore we can approximate $$c(\ce{HA^{2-}})=c(\ce{H3A})\tag8$$ and rewrite $(7)$ as \begin{align} c^2(\ce{H3+O}) &= K_{a_1} \cdot K_{a_2}\\ c(\ce{H3+O}) &= \sqrt{K_{a_1} \cdot K_{a_2}}\\ \ce{pH} &= \frac12\left(\mathrm{p}K_{a_1}+\mathrm{p}K_{a_2}\right). \end{align}

However, this equation only works as a first approximation. Usually the coupled equilibria are very complex and in most instances a computer needs to be involved to calculate it accurately. More information on polyprotic acids.

safety - How does heptafluoropropane suppress fire?

How does heptafluoropropane suppress fire?

It says here that it does so by "inhibiting the chain reaction." What does that mean specifically? Does $\ce{O2}$ attach itself to the heptafluoropropane?

Answer

Curt F. is probably correct in his estimate that heptafluoropropane extinguishes fire primarily by physical means. According to an overview by Choy and Fong, 'An Introduction to Clean Agents: Heptafluoropropane' (Int. J. on Eng. Performance-Based Fire Codes, vol. 5, nr 4, p. 181$-$184, $2003$),

For heptafluoropropane, the contribution of physical mechanisms to the extinguishment of fires predominates over the chemical mechanism. It suppresses fires primarily by

• extracting heat from the flame reaction zone,


• reducing the flame temperature below that which is necessary to maintain sufficiently high reaction rates by a combination of heat of vaporization [and] heat capacity.

They add that,

Oxygen depletion plays an important role in reducing flame temperature. The energy absorbed in decomposing the agent by breaking fluorine bond[s] is quite important, particularly with respect to decomposition production formation.

The chemical effect does indeed involve tying up active radical species. As an example, consider the mixture $\ce{H2/O2}$. The primary active species are $\ce{OH^\bullet}$ radicals.

$$\ce{H2 + O2 -> 2OH^\bullet}$$

The chain starts to grow.

$$\ce{OH^{\bullet} + H2 -> H2O + H^\bullet}$$ $$\tag{two reactive sp. instead of one}\ce{H^{\bullet} + O2 -> OH^{\bullet} + O^\bullet}$$ $$\tag{two reactive sp. instead of one}\ce{O^{\bullet} + H2 -> OH^{\bullet} + H^\bullet}$$

The bottom two steps show especially clearly why fires are violent, quick reactions (after incubation period is over). Heptafluoropropane's chemical extinguishing effect arises from

[----] the thermal decomposition of small amounts of heptafluoropropane in the flame which form fluorinated fragments such as $\ce{CF3}$ and $\ce{CF2}$. These will then consume the key combustion chain-propagating species $\ce{H}$ and $\ce{O}$, but to a lesser extent on $\ce{OH}$ radicals. The rates of chain-branching combustion reaction will decrease, the chemical flame is inhibited and the flame propagation is halted. (Choy, Fong)

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To increase the chemical inhibition, heptafluoropropane (or HFC-227ea) is sometimes mixed with $\ce{NaHCO3}$.

Flame inhibition by sodium species is believed to be due to chemical scavenging of major radical species (e.g., $\ce{OH}$, $\ce{H}$) in the flame.

source: Skaags, 'Assessment of the Fire Suppression Mechanics for HFC-227ea Combined with $\ce{NaHCO3}$', U.S. Army Research Laboratory, link

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One commercial source, unlike Wikipedia, groups pentafluoroethane together with heptafluoropropane.

source: Group of Companies "RealSnabService"

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Further reading, more in-depth discussion and related topics:

• Luo et al.. 'Effect of Hydrofluorocarbons and Perfluorocabons on Suppression Efficiency of $\ce{CH3I}$'. Process Safety and Environment Protection Research Group. link


• Williams, et al.. 'Intermediate Species Profiles in Low Pressure Methane/Oxygen Flames Inhibited by 2-H Heptafluoropropane: Comparison of Experimental Data with Kinetic Modeling'. Annual Conference on Fire Research, $1998$. link


• Sheinson. 'Heptafluoropropane With Water Spray Cooling System As A Total Flooding Halon 1301 Replacement: System Implementation Parameters'. Navy Technology Center for Safety and Survivability. link


• Grosshandler, et al.. 'Extinction of Hydrofluorocarbon Flames with F/H Ratios of Unity and Greater'. Annual Conference on Fire Research, $1998$. link

halacha - Whispering prayers?

Can one whisper t'fila (prayer)? I'm thinking of obligatory t'filos like sh'mone esre and "Sh'ma".

I know one can speak t'fila quietly, even very quietly; in fact, sh'mone esre is said quietly. I'm not asking about loudness versus quietness but specifically about whispering. As Wikipedia notes:

In normal speech, the vocal cords alternate between states of voice and voicelessness. In whispering,… the vocal cords alternate between whisper and voicelessness (though the acoustic difference between the two states is minimal).

In other words, whispering is speaking without the use — or with minimal use — of the vocal cords. All consonants and vowels become largely or completely devoiced. This is independent of loudness: it can be done pretty loudly, and normal speaking can be done quietly.

(The words תִּזְכְּרוּ and תִּשְׂכְּרוּ thus come out almost the same — but not quite. One difference lies in the fact that whispering generally doesn't completely remove voice (as noted in the Wikipedia quotation, above). Another lies in the fact that for some people the place of articulation of a zayin is slightly different than that of a sin, or one is more closed than the other. Also, the preceding chirik may differ slightly, e.g. in length, between the two words. Finally, WAF notes in a comment, below, that people often lengthen normally-voiced consonants when whispering, and suggests that that might suffice to distinguish them from the normally unvoiced ones.)

Is there any source or argument that says that t'fila can or cannot be done in a whisper?

halacha - Bathroom halachos in the bathroom

One may not learn Torah in the bathroom. May one learn Torah that pertains to halachos of the bathroom that came up in the bathroom, or must one leave the bathroom, check the halachah, and return to the bathroom?

Answer

The Rama 85:2 brings down that it is not permitted to learn halachos of bathhouse in a bathhouse, so certainly learning bathroom halachos in the bathroom is prohibited (Bathroom is more strict than a bathhouse)

אפילו להרהר בדברי תורה אסור בבית הכסא ובבית המרחץ ומקום הטינופת והוא המקום שיש בו צואה ומי רגלים.

הגה: ואפילו הלכות המרחץ אסור ללמוד במרחץ (ר"ן פרק כירה ובית יוסף בשם אורחות חיים).

words - Fun with synonyms - "to grab/catch/capture"

Here's a question for you experts. I've actually asked this to my Japanese friends, but I want to see how you guys answer too.

Explain the differences in the following verbs and which one(s) appear more commonly in everyday speech:

1. [掴]{つか}む


2. [捕]{と}る


3. [捕]{と}らえる


4. [捕]{と}らえられる - passive


5. [捕]{つか}まえる


6. [捕]{つか}まえられる - passive


7. [捕]{と}らわれる


8. [捕]{つか}まる - see update below

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Update - 2012/05/08: Looking back at this question after all this time, I knew there was a reason I was including the passive verbs (4 and 6 above). It's because I left a verb out of my original set: [捕]{つか}まる. So then the question with the passives is, what's the difference between 捕まる, 捕らえられる, and 捕まえられる?

Based on @Derek Schaab's answer below, it seems that 捕らえられる would mostly apply to animals/things that "are caught". But which would be the most correct/natural way to say "The criminal was finally caught"?

犯人がやっと(捕まった・捕らえられた・捕まえられた）

Answer

Ignoring the passives, which can be inferred:

• 掴む: grasp. 腕を掴む. The action ends once your hand closes on the object. This is in contrast to 握る, which focuses on the time spent gripping the object after it has been taken in the hand.


• 捕る: capture, as in an animal. 魚を捕る. Can be substituted with 捕獲する. (There are many kanji for とる, the choice of which depends on the object, as I'm sure you know.)


• 捕らえる: (also) capture, or subdue. (But I usually see this written as 捉える, preceded by と, and meaning "perceive, see/recognize/take (as)": 好機と捉える.)


• 捕まえる: prevent something from running away, hold tight to something without any intention of letting go. Can be both physical (犯人を捕まえる) or abstract (人の心を捕まえる).


• 捕らわれる: be bound/taken captive by something (often abstract). 恐怖に捕らわれる.

shemoneh esrei - Bowing for oseh shalom

Why do we bow for oseh shalom in shmoneh esre and kaddish? There are two parts to this:

1. What is the relationship between bowing in general and oseh shalom?


2. What does each direction in which we bow have to do with the corresponding phrase?

Answer

According to the Beit Yosef (OC 123; citing Rav Hai Gaon), the custom is based on the idea that the tefillos correspond to the tamid offerings. When the kohen would go up to the altar, he would go up on the right side, go around, and descend on the left side. We face left first, then right, because we are orienting ourselves according to the Shechina's orientation, which we face when we pray.

Furthermore, the original custom is not exactly to bow in three directions. The Shulchan Aruch writes: "...[A]nd after he takes three steps back, while still bowed forward a bit before straightening up, when he says Oseh shalom bimromav he turns his face to his left, and when he says Hu ya'aseh shalom aleynu he turns his face to his right, and afterwards he bows forward like a servant departing from his master." (OC 123:1) So the bowing part doesn't have much to do with the directions; we simply bow forward in deference to HaShem as we take leave of our prayers.

The custom to do the same at the end of kaddish is stated in Hilchos B'rachos (ibid. 56:5). The Vilna Gaon comments here that he holds that these are extra bows and are forbidden. However, he endorses the bowing at the end of the Shemoneh Esrei, which is originally described in the gemara (Yoma, 53b).

beis hamikdash - If a Kohen donates a kidney is he considered a Bal Moom for purposes of doing an Avodah?

If a Kohen donates a kidney, is he considered a Bal Moom for purposes of doing an Avodah in the future Bais hamikdash? On the one hand, the missing organ is not visible. On the other hand, a cataract is also not visible and I think it would make a Kohen a baal moom.

food - Must I warn people about an untrustworthy restaurant?

What is my obligation to warn fellow kosher observant people about a Restraurant that is claiming to be "Glatt" Kosher, when in fact it has no Rabbinic Supervision at all and the owner's religious observance would not lead you to believe "Glatt" is something he cares about in his home? Does my obligation change any if at one time under a different name he had supervision as a dairy restraurant but had recently reopened in the same location as a meat restraurant?

Answer

First thing I'd do is consult a local rabbi, who may have a better assessment of the situation. Also, if the word does need to be spread that the place is not recommended, it will probably be more effective coming from him. (He's also likely to be better protected if the restaurant sues for defamation or something.)

But for theory's sake (or pretending you're the rabbi): To tell people "restaurant ABC has no rabbinic supervision", or perhaps "restaurant ABC has no rabbinic supervision, and local Rabbi X has said on the record that it's not recommended" would seem to meet all of the criteria required for constructive lashon hara:

1.) You're sure the statement is true (assuming you did your homework!)

2.) You provide only the minimum needed relevant information, in a neutral tone. (Note that I didn't include the owner's personal observance in the examples of permitted statements.)
3.) Your intention is to prevent people from coming to harm (in this case, eating food that's questionably kosher).
4.) No disproportionate harm will befall the subject of your speech. If someone will beat up the restaurant owner, that's disproportionate. If people will just take their business elsewhere because of his lackluster kosher standards, that's perfectly fair.
5.) There's no other way to achieve this goal. That's the tricky one, and why I'd talk with a local rabbi about the situation. There might even be circumstances when you'd talk with the restaurant owner first (if nothing else, to ascertain he's unsupervised), but again, that's best left to a local rabbi.

You or your rabbi might try contacting the webmaster @kashrut.com, who regularly posts alerts of uncertified products and institutions. She has a good sense of how and when this is usually done.

rashi - How do we understand Moshe's rebuke

On Devarim 1:1, Rashi comments that the various places listed are in fact veiled references to episodes in which the Jewish people rebelled. Thus Moshe was offering a kind of concealed rebuke. My questions are:

1. Why is the list of transgressions out of order? The list of rebuke items is not in chronological or any other order that I can ascertain.


2. Why are items left out? Once he's rebuking them, why not point out every time they failed?


3. Why is he rebuking them when they didn't do it? This is not the generation that worshiped the golden calf or sent the spies or complained at the sea. Those people are dead; this is a wholly new generation to whom Moshe seems to be speaking as if they were their parents.